
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 the linear function $f(x) = ax + b$, where $a, b$ are real numbers, $f_1(x) = f(x)$, $f_{n+1}(x) = f(f_n(x))$, for $n=1,2,3,\ldots$. If $f_5(x) = 32x + 31$, then $f_{2008}(-1) =$ ?

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