
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  $99$  space stations. Each pair of space stations is connected by a tunnel. There are  $99$  two-way main tunnels, and all the other tunnels are strictly one-way tunnels. A group of  $4$  space stations is called *connected* if one can reach each station in the group from every other station in the group without using any tunnels other than the  $6$  tunnels which connect them. Determine the maximum number of connected groups.

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