
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 $f(x)=|x-a|+3x$, where $a > 0$.

(1) When $a=1$, find the solution set for the inequality $f(x)\geqslant 3x+2$.

(2) If the solution set for the inequality $f(x)\leqslant 0$ is $\left\{ x\left| x\leqslant -1 \right. \right\}$, find the value of $a$.

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