
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 9 circles connected by 10 straight lines, with each line passing through 3 circles. Players A and B take turns choosing an unchosen circle, with A going first. The player who chooses 3 circles on the same straight line wins. Player A chose circle "1", and player B is able to choose circle "5". To ensure player A wins, the product of all possible next choices for A is?

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