
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]


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Given: The quadratic function about $x$ is $y={x^2}-ax+\frac{a}{2}$ for $0≤x≤1$.<br/>$(1)$ When $a=4$, the maximum value of the function is ____.<br/>$(2)$ If the maximum value of the function is $t$, then the minimum value of $t$ is ____.

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