
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 $f\left( x \right)=\left| x-2\left| + \right|x+a \right|\left( a\in R \right)\right.$.

(1) When $a=1$, find the solution set of the inequality $f\left( x \right)\geqslant 4$;

(2) If the solution set of the inequality $f\left( x \right)\leqslant 2x$ is $\left[ 1,+\infty \right)$, find the value of $a$.

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