
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 $f(x)=|x-a|$.

(1) If $a=2$, solve the inequality: $f(x)\geqslant 3-|x-1|$;

(2) If the solution set of $f(x)\leqslant 1$ is $[2,4]$, and $m+2n=a (m > 0, n > 0)$, find the minimum value of $m^2+4n^2$.

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