
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 $f(x) = |ax-1|$ ($a \in \mathbb{R}$), the solution set of the inequality $f(x) \leq 2$ is $\left\{x \middle| -\frac{1}{2} \leq x \leq \frac{3}{2}\right\}$.
1. Find the value of $a$;
2. Solve the inequality $f(x) + f\left(\frac{x}{2}-1\right) \geq 5$.

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