
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 $f(x)=|ax-1|$ $(a\in R)$, the solution set of the inequality $f(x)\leqslant 2$ is $\\{x|- \frac{1}{2}\leqslant x\leqslant \frac{3}{2}\\}$.

1. Find the value of $a$;
2. Solve the inequality $f(x)+f( \frac{x}{2}-1)\geqslant 5$.

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