
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
Handsome memorized over a hundred words in seven days. The ratio of the number of words memorized in the first three days to the number of words memorized in the last four days is $3:4$, and the ratio of the number of words memorized in the last three days to the number of words memorized in the first four days is $5:6$. How many words did Handsome memorize on the fourth day?

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