
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
A right-angled triangle $ABC$ has points starting simultaneously from vertices $B$ and $C$. One point moves along the hypotenuse $BA=c=85$ meters to point $A$ at a speed of $8.5$ meters/second, while the other point moves along leg $CA=b=75$ meters to point $A$ at a speed of $5$ meters/second. Determine when the distance between the two points will be $26$ meters. (Without using trigonometry!)

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