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

--- LLM ---
  None

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

--- LLM ---
  None

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

--- LLM ---
  None

### SYSTEM: calling tool
  (1, 2, 3) → "incline"

--- LLM ---
  None

### SYSTEM: calling tool
  (3, 2, 1) → "decline"

--- LLM ---
  None

### SYSTEM: calling tool
  (3, 1, 2) → "valley"
  (1, 1, 2) → "incline"
  (1, 2, 2) → "incline"
  (2, 2, 1) → "decline"
  (2, 1, 1) → "decline"
  (2, 2, 2) → "plateau"
  (-1, 0, 1) → "incline"
  (-1, -2, -3) → "decline"
  (0, 0, 1) → "incline"
  (1, 0, 0) → "decline"

--- LLM ---
  None

### SYSTEM: calling tool
  (2, 3, 2) → "mountain"
  (2, 1, 2) → "valley"
  (1, 0, 2) → "valley"
  (2, 2, 3) → "incline"
  (3, 2, 2) → "decline"
  (0, 1, 1) → "incline"

--- LLM ---
  I’ve determined the function classifies the shape formed by three numbers (a, b, c) based on their relative order:

  - plateau: a == b == c
  - incline: a <= b <= c and not all equal (nondecreasing with possible ties)
  - decline: a >= b >= c and not all equal (nonincreasing with possible ties)
  - mountain: a < b and b > c (strict local maximum at the middle)
  - valley: a > b and b < c (strict local minimum at the middle)

  Notes:
  - Mountain/valley require strict inequalities on both sides of b.
  - If there are ties on one side (e.g., a == b < c or a < b == c), it’s treated as incline; similarly for decline.

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

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

### SYSTEM: inputs:
  {'a': 2, 'b': 1, 'c': 3}

--- LLM ---
  Since a > b and b < c, the sequence forms a strict local minimum at the middle, which the function labels as 'valley'.

  `valley`

### SYSTEM: CORRECT

### SYSTEM: inputs:
  {'a': 1, 'b': 5, 'c': 2}

--- LLM ---
  Since a < b and b > c, the middle value is a strict local maximum, i.e., a mountain.

  `mountain`

### SYSTEM: CORRECT

### SYSTEM: inputs:
  {'a': 4, 'b': 4, 'c': 4}

--- LLM ---
  All three values are equal, which matches the plateau case in the inferred rules.

  `plateau`

### SYSTEM: CORRECT

### SYSTEM: inputs:
  {'a': 1, 'b': 2, 'c': 3}

--- LLM ---
  Based on the established rules: a <= b <= c and not all equal classifies as 'incline'. For (1,2,3), it’s strictly increasing.

  `incline`

### SYSTEM: CORRECT