
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
Lucy begins a sequence with the first term at 4. Each subsequent term is generated as follows: If a fair coin flip results in heads, she triples the previous term and then adds 3. If it results in tails, she subtracts 3 and divides the result by 3. What is the probability that the fourth term in Lucy's sequence is an integer?
A) $\frac{1}{4}$
B) $\frac{1}{2}$
C) $\frac{3}{4}$
D) $\frac{7}{8}$

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