
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
Define the function iteration: $f^{(0)}(x)=x$ $f^{(1)}(x)=f\left(x\right)$ $f^{(2)}(x)=f\left(f\left(x\right)\right)$ $\cdots$ $f^{(n+1)}(x)=f(f^{(n)}(x))$ Given $f\left(x\right)=3x+2$, determine the formula for $f^{(n)}(x)$.

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