
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 prime number of the form \( 2^{p} - 1 \) is called a Mersenne prime, where \( p \) is also a prime number. To date, the largest known Mersenne prime is \( 2^{82589933} - 1 \). Find the last two digits of this number.

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