
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
In a new sequence of positive integers, Jane starts with a number and applies different rules depending on the nature of the number:
1. If the integer is less than 20, multiply it by 3.
2. If the integer is even and between 20 and 60, add 10 to it.
3. If the integer is even and greater than 60, divide it by 5.
4. If the integer is odd and greater than 20, subtract 7 from it.

Starting with the number 120, determine the $50^\text{th}$ term in the sequence.
A) 12
B) 66
C) 36
D) 56

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