
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 $f(x) = |2x - a| + |2x - 1|$ where $a \in \mathbb{R}$.
1. When $a = -1$, find the solution set for $f(x) \leq 2$.
2. If the solution set of $f(x) \leq |2x + 1|$ contains the set $[\frac{1}{2}, 1]$, find the range of real number $a$.

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