
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
Shuai Shuai finished memorizing English words in five days. It is known that he memorized $\frac{1}{2}$ of the total words in the first three days, $\frac{2}{3}$ of the total words in the last three days, and memorized 120 fewer words in the first three days than in the last three days. How many English words did Shuai Shuai memorize on the third day?

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