
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
If the function \( f(x) = -\frac{1}{2}x^2 + \frac{13}{2} \) has a minimum value of \( 2a \) and a maximum value of \( 2b \) on the interval \([a, b]\), find \([a, b]\).

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