
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
The graph of the function \( f(x) \) is shown below. How many values of \( x \) satisfy \( f(f(x)) = 4 \)? Assume the graph is identical to the one shown in the original problem but adjustments in the constant values have changed where \( f(x) = 4 \) occurs.

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