
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 
\[ f(n) = 
\begin{cases} 
n^2 + 1 & \text{if } n < 3, \\
3n + 2 & \text{if } 3 \leq n < 6, \\
2n - 1 & \text{if } n \geq 6.
\end{cases}
\]
Find $f(f(f(1)))$.

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