
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
There are 130 trees planted in a circle: birches and linden trees (both types are present). Each tree has a sign saying: "Two different trees are growing next to this tree." It is known that this statement is false for all linden trees and for exactly one birch tree. How many birches could have been planted? Indicate all possible options.

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