
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 the parameterized equation of curve $C\_1$ as $\{\_{y=4+5\sin t}^{x=5+5\cos t}(t$ is the parameter$).\; $Establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of curve $C\_2$ is $\rho =2\cos \theta \;$.
(1) Convert the parameterized equation of $C\_1$ into a polar coordinate equation.
(2) Find the polar coordinates of the intersection points of $C\_1$ and $C\_2$ $(\rho \geqslant 0,0\leqslant \theta < 2\pi ).\; $

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