
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 plane rectangular coordinate system $xOy$, the parametric equations of curve $C_{1}$ are $\left\{{\begin{array}{l}{x=1+\cos\varphi}\\{y=\sin\varphi}\end{array}}\right.$ ($\varphi$ is the parameter), and the general equation of line $C_{2}$ is $x+y=3$. Establish a polar coordinate system with $O$ as the pole and the positive $x$-axis as the polar axis.<br/>$(1)$ Find the polar coordinate equations of $C_{1}$ and $C_{2}$;<br/>$(2)$ In the polar coordinate system, the rays $θ=α$ ($0<α<\frac{π}{2}$) intersect $C_{1}$ and $C_{2}$ at points $A$ and $B$ (different from the pole), respectively. If $|OA|\cdot |OB|=3$, find the value of $\alpha$.

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