
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 (birches and lindens) are planted in a circle. On each tree, there is a sign that says: "Two different trees are growing next to this tree." It is known that the sign is incorrect on all lindens and exactly one birch. How many birches could have been planted? List all possible variants.

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