
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 pile contains 6468 pearls. If you take a prime number of pearls each time, and after several times you take exactly all of them, there are \( a \) different ways to do this. If you take an odd number of pearls each time, and after several times you take exactly all of them, there are \( b \) different ways to do this. What is \( a + b = \)? (Each time, the number of pearls taken is the same)

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