
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 quadratic function $y = f(x)$ achieves its minimum value of $-3$ at $x = -1$, and satisfies $f(2) = \frac{15}{4}$.  
(1) Find the analytical expression of the function $y = f(x)$.  
(2) When the minimum value of the function $y = f(x)$ on the interval $[-2m + 3, -m + 2]$ (where $m > 1$) is $- \frac{9}{4}$, solve for the value of $m$.

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