
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
Thirty switches in a network are to be connected so that each switch has a direct connection to exactly four other switches, ensuring that no switch connects more than once to any other switch. How many connections will be necessary?

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