
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 Cartesian coordinate system $(xOy)$, the parametric equation of line $l$ is given by $\begin{cases} x=\sqrt{3}t, \\ y=t \end{cases}(t\text{ is a parameter})$, and the polar coordinate system is established by taking the coordinate origin $O$ as the pole, the non-negative semi-axis of the $x$-axis as the polar axis, and the same length unit as the Cartesian coordinate system $(xOy)$. The polar equation of curve $C$ is obtained as $\rho^{2}=\cos ^{2}\theta+\sin \theta(\rho\geqslant 0)$.

(1) If line $l$ intersects curve $C$ at points $A$ and $B$, find the length of line segment $AB$;

(2) If $M$ and $N$ are two points on curve $C$, and $OM \perp ON$, find the maximum value of the length of line segment $MN$.

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