
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
Elisa creates a sequence in a manner similar to Jacob but starts with the first term as 10. Each succeeding term depends on the outcome of flipping a fair coin: If it lands heads, the next term is obtained by doubling the previous term and subtracting 1; if it lands tails, the next term is half of the previous term, subtracting 1. What is the probability that the fourth term in Elisa's sequence is an integer?
A) $\frac{1}{4}$
B) $\frac{1}{3}$
C) $\frac{1}{2}$
D) $\frac{3}{4}$
E) $\frac{5}{8}$

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