
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
Two companies take turns hiring programmers, among which there are 11 geniuses. Each company chooses its first programmer randomly, and each subsequent one must be familiar with someone previously hired by that company. If a company cannot hire a programmer according to these rules, it stops hiring, and the other company may continue. The list of programmers and their acquaintances is known in advance, including information about who the geniuses are. Can the acquaintances be arranged in such a way that the company entering the game second can hire 10 geniuses, no matter how the first company acts?

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