### SYSTEM: interrogating function with args ['integer', 'integer', 'integer']

--- LLM ---


### SYSTEM: calling tool
  (0, 0, 0) → "1"
  (1, 1, 1) → "2"
  (1, 2, 3) → "5"
  (2, 1, 3) → "5"
  (3, 2, 1) → "5"
  (1, 3, 2) → "5"
  (-1, -2, -3) → "7"
  (1, -2, 3) → "5"
  (100, 200, 300) → "599"
  (5, 0, 8) → "12"

--- LLM ---


### SYSTEM: calling tool
  (1, 1, 0) → "1"

--- LLM ---


### SYSTEM: calling tool
  (1, 0, 0) → "secretff2a"

--- LLM ---


### SYSTEM: calling tool
  (-1, 0, 0) → "2"

--- LLM ---


### SYSTEM: calling tool
  (-1, -1, 0) → "3"

--- LLM ---


### SYSTEM: calling tool
  (-1, -1, -1) → "4"

--- LLM ---


### SYSTEM: calling tool
  (1, 1, -1) → "2"

--- LLM ---


### SYSTEM: calling tool
  (1, -1, 0) → "1"

--- LLM ---


### SYSTEM: calling tool
  (2, 3, 4) → "8"

--- LLM ---


### SYSTEM: calling tool
  (-2, -3, -4) → "10"

--- LLM ---


### SYSTEM: calling tool
  (2, 3, -4) → "8"

--- LLM ---
  After a series of tests, I have determined the behavior of the mystery function. It appears to operate based on the
  signs of the input integers. The function is commutative, meaning the order of the inputs `a`, `b`, and `c` does not
  affect the result.

  Here is a summary of the function's logic:

  *   **If all inputs are non-negative (0 or greater):**
      *   If `a`, `b`, and `c` are all 0, the function returns `1`.
      *   If `a=1`, `b=0`, and `c=0` (or any permutation), the function returns a special string value `'secretff2a'`.
      *   In all other cases, the function returns the sum of the inputs minus 1. (e.g., `mystery_function(1, 2, 3)`
  returns `1 + 2 + 3 - 1 = 5`).

  *   **If there are any negative inputs:**
      *   The function first calculates the sum of the inputs (`S = a + b + c`).
      *   If the sum `S` is negative, the function returns the sum of the absolute values of the inputs plus 1 (i.e.,
  `abs(a) + abs(b) + abs(c) + 1`).
      *   If the sum `S` is zero or positive, the function returns the sum of the absolute values of the inputs minus 1
  (i.e., `abs(a) + abs(b) + abs(c) - 1`).

  This set of rules consistently explains the results of all 20 tests performed.

### SYSTEM: The tool was used 20 times.

### SYSTEM: verifying function with args ['integer', 'integer', 'integer']

### SYSTEM: inputs:
  {'a': 1, 'b': 0, 'c': 0}

--- LLM ---
  The user is testing my hypothesis about the mystery function with the input `{'a': 1, 'b': 0, 'c': 0}`. Based on my
  previous tests, specifically test number 12 (`mystery_function(a:1, b:0, c:0)`), I identified a special case. When all
  inputs are non-negative, and exactly one input is 1 while the others are 0, the function returns the specific string
  'secretff2a'. The provided input fits this exact condition. Therefore, I predict the output will be this special
  string.

  `secretff2a`

### SYSTEM: CORRECT