
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
(10 points) Let $f(x)=|x|-|2x-1|$, and denote the solution set of $f(x) > -1$ as $M$.

(1) Find the set $M$; (2) Given $a \in M$, compare the values of $a^2-a+1$ and $\frac{1}{a}$.

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