
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 a quadratic function $f(x)$ that satisfies $f(1) = 1$, and $f(x+1) - f(x) = 4x - 2$.
(1) Find the explicit formula of $f(x)$;
(2) If $f(x)$ is not monotonic on the interval $[2a, a+1]$, find the range of the real number $a$.

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