
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 that the minimum value of the quadratic function $f(x)$ is $1$, and $f(0)=f(2)=3$
(1) Find the analytical expression of $f(x)$;
(2) If the graph of $y=f(x)$ is always above the graph of $y=2x+2m+1$ when $x \in [-3,-1]$, determine the range of values for the real number $m$.

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