
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given that the side lengths of triangle \( \triangle ABC \) are all integers, \( \cos A = \frac{11}{16} \), \( \cos B = \frac{7}{8} \), and \( \cos C = -\frac{1}{4} \), determine the smallest possible value of the perimeter of \( \triangle ABC \).

Present the answer in LaTex format: \boxed{Your answer}
user