
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 rectangular coordinate system $xoy$, the rectangular coordinate equation of the curve $C_1$ is $x^2+y^2-2y=0$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar coordinate equation of the curve $C_2$ is $\rho\sin^2\theta=4\cos\theta$.
(1) Find the polar coordinate equation of $C_1$ and the rectangular coordinate equation of $C_2$;
(2) Given that the rectangular coordinate equation of ray $l$ is $y=\frac{3}{4}x (x\geq 0)$, if ray $l$ intersects $C_1$ and $C_2$ at points $A$ and $B$ respectively, find the value of $|OA|\cdot|OB|$.

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