
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
There is a circle $k$ and a point $P$ outside it. The secant $s$ passing through $P$ intersects $k$ at points $B$ and $C$, with $B$ on the segment $PC$. Construct the position of $s$ such that $BC \cdot PC = d^{2}$, where $d$ is a given segment.

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