
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 $f(x) = |x-a|$ ($a \in \mathbb{R}$).
1. When $a=1$, solve the inequality $f(x) < |2x-1|-1$.
2. When $x \in (-2, 1)$, solve $|x-1| > |2x-a-1| - f(x)$ for the range of $a$.

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