
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
Given Jerry starts at 0 on the real number line, he tosses a fair coin 10 times, and for each toss, he moves 1 unit in the positive direction for heads and 1 unit in the negative direction for tails. Find the probability that he reaches 6 units at some time during these tosses, and represent it as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are coprime.

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