
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
In a meadow, ladybugs have gathered. If a ladybug has six spots on its back, it always tells the truth. If it has four spots, it always lies. There are 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, "Together we have 30 spots in total." The third disagreed, saying, "Altogether, we have 26 spots on our backs." "Of these three, exactly one told the truth," declared each of the remaining ladybugs. How many ladybugs were there in total in the meadow?

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