
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
Let $f$ be the function defined by $f(x) = -3 \cos(\pi x/2)$. Determine the number of values of $x$ such that $-3 \le x \le 3$ that satisfy the equation $f(f(f(x))) = f(x)$.

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