
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 the function $f(x)=|x-2|+|x+1|$.
(1) Find the solution set for the inequality $f(x) > 7$.
(2) If $m$ is a real number, $n > 0$, and the minimum value of $f(x)$ is $m+n$, find the minimum value of $m^{2}+n^{2}$ and specify the values of $m$ and $n$ at this time.

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