
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
A space station has 99 pods. Every pair of pods is connected by a tube. 99 tubes are two-way, and the others are all one-way. What is the largest number of sets of 4 pods that can be fully communicating (so that one can go between any two pods of the set without going outside the four pods and their six tubes)?

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