
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 the graph of the function $f(x)$ below, determine how many values of $x$ satisfy $f(f(x)) = 4$. The function segments are described as follows:
- For $-4 \leq x < -1$, $f(x) = -x - 3$.
- For $-1 \leq x < 3$, $f(x) = x + 2$.
- For $3 \leq x \leq 5$, $f(x) = -x + 7$.

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