
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
There are 130 trees planted in a circle: birches and linden trees (both types are present). Each tree has a sign that reads: "Two different trees grow next to it." It is known that the sign is false for all the linden trees and exactly one birch. How many birches could there be? List all possible options.

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