
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 \( f(x) \), determine how many values of \( x \) satisfy \( f(f(x)) = 5 \). Assume from the graph:
- \( f(x) \) increases linearly from \( x = -4 \) to \( x = 0 \) and from \( x = 3 \) to \( x = 5 \).
- \( f(x) \) is constant at a value of 5 from \( x = 0 \) to \( x = 3 \).
- There are no \( x \) values such that \( f(x) = -3 \).

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