
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 $f(x)=|x|-2|x+3|$,
(1) Solve the inequality $f(x)\geqslant 2$;
(2) If there exists $x\in\mathbb{R}$ such that the inequality $f(x)-|3t-2|\geqslant 0$ holds, find the range of the parameter $t$.

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