
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
Harry is generating a sequence of positive integers by adjusting the rules Terri used.  He starts with a positive integer, then applies the modified rules to the result as follows:

Rule 1: If the integer is less than 10, multiply it by 7.
Rule 2: If the integer is greater than or equals to 10 and even, divide it by 3.
Rule 3: If the integer is greater than or equals to 10 and odd, subtract 3 from it.

Starting with the integer 120, what is the $100^\text{th}$ term in Harry's sequence?
A) 4
B) 6
C) 14
D) 28
E) 42

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