
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 of a two-dimensional grid. He tosses a fair coin $10$ times. With each heads, he moves one unit up, and with each tails, he moves one unit down. Determine the probability that at any time during the tosses, Jerry reaches or crosses 4 units up from the origin. Express your answer as a fraction $\frac{p}{q}$, where $p$ and $q$ are coprime integers.
A) $\frac{15}{64}$
B) $\frac{7}{32}$
C) $\frac{120}{1024}$
D) $\frac{1}{2}$
E) $\frac{28}{256}$

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