
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 $y=-(x-h)^2$ (where $h$ is a constant), and the independent variable $x$ ranges from $2$ to $5$.<br/>$(1)$ When $h=3$, the maximum value of the function is ______;<br/>$(2)$ If the maximum value of the function is $-1$, then the value of $h$ is ______.

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