
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 
\[ 
f(x) =
\begin{cases}
3x/2 &\quad \text{if } x \text{ is even}, \\
2x+1 &\quad \text{if } x \text{ is odd}.
\end{cases}
\]
What is \( f(f(f(f(1)))) \)?

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