
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 set  $S$  has  $7$  elements. Several  $3$ -elements subsets of  $S$  are listed, such
that any  $2$  listed subsets have exactly  $1$  common element. What is the maximum number of subsets that can be listed?


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