
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
The meaning of the symbol max{a, b} is: if $a \geq b$, then $max\{a, b\} = a$; if $a < b$, then $max\{a, b\} = b$. For example, $max\{-1, -3\} = -1$, $max\{3, 5\} = 5$. Then, the minimum value of $max\{x^2, x+2\}$ is.

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