
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
Alice and Bob are playing a new version of the Smallest Positive Integer Game. This time, Alice says, "My number is 36." Bob must now choose a number such that every prime factor of his number must be a prime factor of Alice’s number, but his number must also be twice a prime. What is the smallest possible number Bob could choose?

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