
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 \( f(f(x)) = 5 \). The function is defined piecewise, as seen on the graph which shows three segments of lines connecting points \( (-4, 4), (-1, 1), (3, 5) \), and \( (5, 3) \).

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