
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 flock of pigeons flew up to a tall tree. Some pigeons perched on the branches, while others stayed under the tree. The pigeons on the branches said to those below: "If one of you were to fly up to us, you would be three times fewer than all of us together, but if one of us were to fly down to you, we would be equal in number." How many pigeons were perched on the branches, and how many were under the tree? (From the Tales of the Thousand and One Nights. Night 458)

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