
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
Marie uses a procedure to create a sequence of numbers, starting with the first term as 7. She rolls a fair three-sided die labeled 1, 2, and 3 for each term after the first. If it comes up 1, she triples the previous term and subtracts 2; if it comes up 2, she doubles the previous term and subtracts 1; if it comes up 3, she divides the previous term by 2 and subtracts 1. Determine the probability that the fourth term in Marie's sequence is an integer.

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