
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
Jacob starts a new sequence of numbers with the first term set as 8. He follows these steps to generate each succeeding term: If he flips heads, he doubles the previous term and subtracts 1. If he flips tails and it is the first or third instance of tails, he takes half of the previous term and subtracts 1. If he flips tails twice consecutively, he triples the previous term and subtracts 2. What is the probability that the fourth term in Jacob's sequence is an integer?
A) $\frac{4}{7}$
B) $\frac{1}{3}$
C) $\frac{1}{2}$
D) $\frac{5}{8}$
E) $\frac{3}{4}$

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