
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: "Two different trees are growing nearby." It is known that the sign is false on all lindens and exactly on one birch. How many birches could have been planted? Specify all possible options.

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