
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
Reading comprehension: Find the minimum value of the algebraic expression $y^2 + 4y + 8$. Solution: Since $y^2 + 4y + 8 = (y^2 + 4y + 4) + 4 = (y + 2)^2 + 4 \geq 4$, when $y = -2$, the minimum value of the algebraic expression $y^2 + 4y + 8$ is $4$.

Following application (1): Find the minimum value of the algebraic expression $m^2 + 2m + 3$.

Following application (2): Find the maximum value of the algebraic expression $-m^2 + 2m + 3$.

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