
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
For all complex numbers \( z \), define the function \( f(z) \) as follows:
\[
f(z) = \left\{
\begin{array}{cl}
z^{2} & \text{ if } z \text{ is not real}, \\
-z^2 & \text{ if } z \text{ is real}.
\end{array}
\right.
\]
Find \( f(f(f(f(2+i)))) \).

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