
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
The number 770 is written on a blackboard. Melody repeatedly performs moves, where a move consists of subtracting either 40 or 41 from the number on the board. She performs moves until the number is not positive, and then she stops. Let \( N \) be the number of sequences of moves that Melody could perform. Suppose \( N = a \cdot 2^b \) where \( a \) is an odd positive integer and \( b \) is a nonnegative integer. Compute \( 100a + b \).

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