
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
Does the function \( f(x) = x^{2} + 3 \) satisfy the conditions of the Mean Value Theorem on the interval \([-1, 2]\)? If the theorem is applicable, find the point \( c \) where \( f(b) - f(a) = f'(c)(b - a) \), where \( a = -1 \) and \( b = 2 \).

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