
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
130 trees are planted in a circle: birches and lindens (both types are present). Each tree has a sign that reads: "Next to this tree, two different trees grow." It is known that all the lindens have false statements and exactly one birch has a false statement. How many birches could have been planted? List all possible options.

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