
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
Given a function $f(x)$ defined on the complex number set $\mathbb{C}$ that satisfies 
$$
f(x) = \begin{cases} 
1+x, & x\in\mathbb{R} \\ 
\frac{1-i}{|i|}x, & x\notin\mathbb{R}
\end{cases}
$$
(where $i$ is the imaginary unit), calculate $f(f(1+i))$.

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