
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
In the history of mathematics, the locus of points in a plane where the product of the distances to two fixed points is a constant is called a Cassini oval. In the Cartesian coordinate system $xOy$, let the moving point be $P(x,y)$ and the two fixed points be $F_{1}(-1,0)$ and $F_{2}(1,0)$. If the product of the distances from point $P$ to the two fixed points is equal to $2$, and after simplification, the curve $C:x^2+y^2+1=2\sqrt{x^2+1}$ is obtained, then the maximum value of $OP$ is ______.

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