
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 person flips a coin and scores $a$ points for heads and $b$ points for tails, where $a$ and $b$ are positive integers, and $a > b$. The person accumulates the score with each coin flip. They notice that regardless of the number of flips, there are exactly 35 scores that cannot be recorded. For example, 58 is one such score. Determine the values of $a$ and $b$. (32nd Annual Putnam Mathematical Competition, 1971)

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