
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 $f(x)= \sqrt{|x+1|+|x-3|-m}$ whose domain is $R$.

(1) Find the range of values for $m$.

(2) If the maximum value of $m$ is $n$, solve the inequality $|x-3|-2x \leqslant 2n-4$ with respect to $x$.

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