
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
Determine the functions \( f: \mathbb{Z} \rightarrow \mathbb{Z} \) such that, for all integers \( m \) and \( n \):

\[ 
f(m + f(f(n))) = -f(f(m + 1)) - n 
\]

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