
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 limes (both species are present). Each tree has a sign that reads: "Two different trees grow next to me." It is known that this statement is false for all limes and exactly one birch. How many birches could have been planted? Indicate all possible options.

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