
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 $A = (0, 5)$ and $B = (0, 15)$. Points $A'$ and $B'$ are on the line $y = x$, and lines $\overline{AA'}$ and $\overline{BB'}$ intersect at point $C = (3, 7)$. Find the length of $\overline{A'B'}$.

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