
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
Ladybugs gathered in a meadow. If a ladybug has six spots on its back, it always tells the truth, and if it has four spots, it always lies. There were no other types of ladybugs in the meadow. The first ladybug said, "Each of us has the same number of spots on our back." The second said, "Altogether, there are 30 spots on our backs." The third contradicted, "No, altogether there are 26 spots on our backs." "Among these three, exactly one is telling the truth," stated each of the remaining ladybugs. How many ladybugs gathered in the meadow?

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