
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 circle $C$: $x^{2}+y^{2}+2x-4y+3=0$, let point $A(0,a)$ where $(a > 0)$. If there exists a point $M$ on circle $C$ such that $MA=\sqrt{2} MO$, then the range of $a$ is __________.

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