
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
Daniel creates a sequence of numbers beginning with the first term of 8. Each subsequent term is generated by flipping a fair coin. If the coin lands on heads, the next term is three times the previous term minus 2. If it lands on tails, he takes half of the previous term and subtracts 1. What is the probability that the fourth term in Daniel's sequence is an integer?
A) $\frac{1}{8}$
B) $\frac{1}{4}$
C) $\frac{1}{2}$
D) $\frac{3}{4}$
E) $\frac{7}{8}$

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