
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
Jerry starts at the origin $O$ on the number line and flips a fair coin 8 times. Each time the coin lands heads, he moves one unit in the positive direction; if it lands tails, he moves one unit in the negative direction. If the probability that he ends up at coordinate 4, calculate the value of $a+b$ where the probability is given by $\frac{a}{b}$ with $\gcd(a,b) = 1$.

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