
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
Wu starts out with exactly one coin. Wu flips every coin he has *at once* after each year. For each heads he flips, Wu receives a coin, and for every tails he flips, Wu loses a coin. He will keep repeating this process each year until he has  $0$  coins, at which point he will stop. The probability that Wu will stop after exactly five years can be expressed as   $\frac{a}{2^b}$ , where  $a, b$  are positive integers such that  $a$  is odd. Find  $a+b$ .

*Proposed by Bradley Guo*

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