
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 subset of a student group is called an *ideal company* if
1) in this subset, all girls are liked by all young men,
2) no one can be added to this subset without violating condition  $1$ .
In a certain group,  $9$  female students and  $15$  students study. Warden of the group made a list of all kinds of ideal companies in this group. What is the largest number of companies on this list?

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