
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 $f(x)=|x+2a|+|x-1|$.

(1) If $a=1$, solve the inequality $f(x)\leqslant 5$;

(2) When $a\ne 0$, $g(a)=f(\frac{1}{a})$, find the range of $a$ that satisfies $g(a)\leqslant 4$.

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