
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 \( g \) be the function defined by \( g(x) = -3 \cos(2\pi x) \). How many values of \( x \) such that \( -1 \le x \le 1 \) satisfy the equation \( g(g(g(x))) = g(x) \)?

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