
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 the line $p$ be the perpendicular bisector of points $A = (30, 10)$ and $B = (6, 6).$ Given that $AB$ meets $p$ at $C = (x, y),$ calculate the value of $3x - 5y$.

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