
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
Five prime numbers are randomly selected without replacement from the first twelve prime numbers. What is the probability that the sum of the five selected numbers is even? Here the extra condition is the list of first twelve prime numbers now includes one added even prime: 2 and a newly considered primes 31 and 37.

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