
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 the function \( f(x) = 2x^2 - ax + 5 \), where \( x \in [-1, 2] \).
1. When \( a = 4 \), find the extreme value of \( f(x) \).
2. If the minimum value of \( f(x) \) is -5, find the value of the real number \( a \).

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