
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 that $F(\sqrt{6},0)$ is the right focus of the ellipse $C:\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1(a>b>0)$, the line $l$ passing through point $F$ intersects the ellipse $C$ at points $A$ and $B$, with $P$ being the midpoint of $AB$ and $O$ being the origin. If $\triangle OFP$ is an isosceles triangle with $OF$ as the base and the circumcircle of $\triangle OFP$ has an area of $2\pi$, then the length of the major axis of the ellipse $C$ is ______.

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