
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
Reading from left to right, a sequence consists of 6 X's, followed by 24 Y's, followed by 96 X's. After the first n letters, reading from left to right, one letter has occurred twice as many times as the other letter. Find the sum of the four possible values of n.

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