
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
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 \\(\dfrac{1}{a}\\).

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