
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 a polar coordinate system with the pole at the origin \\(O\\) of the Cartesian coordinate system, and the polar axis coinciding with the non-negative half of the \\(x\\)-axis, the curve \\(C_{1}\\): \\(\rho\sin^{2}\theta=4\cos\theta\\), and \\(C_{2}\\): \\(\begin{cases} x=1+t\cos\theta \\ y=t\sin\theta \end{cases}\\) (where \\(t\\) is a parameter), intersect at points \\(A\\) and \\(B\\). If the area of \\(\triangle AOB\\) is \\(\sqrt{6}\\), then \\(|AB|=\\) \_\_\_\_\_\_.

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