
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 parametric equations of the curve $C$ are given by $$\begin{cases} x=1+2\cos\theta \\ y=2\sin\theta \end{cases}$$ (where $\theta$ is the parameter). Establish a polar coordinate system with the coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of line $l$ is given by $\rho(\cos\theta+\sin\theta)=m$ ($m>0$).

1. Find the polar equation of curve $C$.
2. If line $l$ intersects with the line $\theta=\frac{\pi}{4}$ ($\rho\in\mathbb{R}$) at point $A$ and intersects with curve $C$ at points $M$ and $N$, and $|OA|\cdot|OM|\cdot|ON|=6$, find $m$.

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