
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
Around a circle, 130 trees are planted: birches and lindens (both types are present). Each tree has a sign that reads: "Next to it, two different types of trees are growing." It is known that among all the trees, this statement is false for all lindens and exactly one birch. How many birches could there be? List all possible options.

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