
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
(The full score of this question is 12 points) The minimum value of the quadratic function $f(x)$ is 1, and $f(0) = f(2) = 3$.

(1) Find the expression of $f(x)$;

(2) If $f(x)$ is not monotonic in the interval $[2a, a + 1]$, find the range of values for $a$.

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