
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 \(f(z)\) as:
\[ f(z) = \left\{
\begin{array}{cl}
z^{2} + 1 &\text{ if } z \text{ is not real}, \\
-z^2 - 1 &\text{ if } z \text{ is real}.
\end{array}
\right.\]
Find \(f(f(f(f(f(1+i)))))\).

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