
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 6 spots on its back, it always tells the truth; if it has 4 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 backs." The second said, "Altogether, we have 30 spots on our backs." The third countered, "No, altogether we have 26 spots on our backs." Each of the remaining ladybugs declared, "Exactly one of the three statements is true." How many ladybugs are in the meadow in total?

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