
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 $f(x)=x^{2}+2x$, the maximum value of $M$ among all real numbers $M$ that make $f(x) \geqslant M$ true is called the lower bound of the function $f(x)=x^{2}+2x$. For $a \in R$ and $a \neq 0$, the lower bound of $a^{2}-4a+6$ is _______.

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