
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 $m, n \in \mathbb{Z}$, given that the function $f(x) = \log_{2}(-|x|+4)$ has a domain of $[m, n]$ and a range of $[0, 2]$. If the equation $2^{|1-x|} + m + 1 = 0$ has a unique real solution for $x$, then find the value of $m+n$.

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