
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
For the function $f(x) = x^2 + 2x$, among all real numbers $M$ that satisfy $f(x) \geq M$, we call the greatest value of $M$, $M_{\text{max}}$, the infimum of the function $f(x) = x^2 + 2x$. Then, for $a \in \mathbb{R}$ and $a \neq 0$, the infimum of $a^2 - 4a + 6$ is.

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