
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
Let  $a,b,c$  be non-zero real numbers. The lines  $ax + by = c$  and  $bx + cy = a$  are perpendicular and intersect at a point  $P$  such that  $P$  also lies on the line  $y=2x$ . Compute the coordinates of point  $P$ .

*2016 CCA Math Bonanza Individual #6*

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