
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
Ella uses the following rules to write down a sequence of numbers. She chooses the first term to be 5. To generate each succeeding term, she flips a fair coin. If it comes up heads, she triples the previous term and adds 2. If it comes up tails, she divides the previous term by 3 and subtracts 2. What is the probability that the fourth term in Ella's sequence is an integer?
A) \( \frac{1}{4} \)
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}
user