
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 Sarah starts at $0$ on the real number line and tosses a fair coin $10$ times, where she moves $1$ unit in the positive direction when she gets heads and $1$ unit in the negative direction when she gets tails, calculate the probability that she reaches exactly $5$ at some point during her tosses and returns to $0$ by the end of her $10$ tosses.

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