
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 circle $C\_1$ with center $C\_1$ and a point $A(2,4)$ on the circle. The equation of circle $C\_1$ is $	(x-6)^2+(y-7)^2=25$.
(1) Find the standard equation of circle $C\_2$ which is tangent to the $x$-axis, externally tangent to circle $C\_1$, and whose center $C\_2$ lies on the line $x=6$.
(2) Let line $l$ be parallel to $OA$ intersecting circle $C\_1$ at points $B$ and $C$, such that $|BC|=|OA|$. Find the equation of line $l$.

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