
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
On two opposite banks of a river stand two palm trees. The height of one is 20 cubits, the other is 30 cubits. The width of the river is 50 cubits. At the top of each palm tree sits a bird. Both birds see a fish in the river and simultaneously fly in a straight line towards it, reaching the surface of the water at the same time at a point on the line connecting the roots of the palm trees. Determine the lengths of the paths flown by the birds and the location of their meeting point.

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