
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 creates a new sequence using the following rules: He starts with the number 8. In each subsequent term, if he flips a coin and it comes up heads, he triples the previous term and subtracts 2; if it comes up tails, he halves the previous term and subtracts 1. What is the probability that the fifth term in Jacob's sequence is an integer if all coin flips result in heads?
A) \( \frac{1}{8} \)
B) \( \frac{1}{16} \)
C) \( \frac{1}{32} \)
D) \( \frac{1}{64} \)
E) \( \frac{1}{128} \)

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