
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
Mae starts with a sequence where the first term is 8. For each subsequent term, she flips a fair coin. If it comes up heads, she triples the previous term and then subtracts 2. If it comes up tails, she takes one-third of the previous term and subtracts 1. What is the probability that the fourth term in Mae's sequence is an integer?
A) \(\frac{1}{16}\)
B) \(\frac{1}{8}\)
C) \(\frac{1}{4}\)
D) \(\frac{1}{2}\)

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