
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 \(A=(0,10)\) and \(B=(0,15)\). Points \(A'\) and \(B'\) are on the line \(y=x\), and \(\overline{AA'}\) and \(\overline{BB'}\) intersect at \(C=(3,9)\). What is the length of \(\overline{A'B'}\)?

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