
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
Using only the digits 1, 2, 3, 4, and 5, Peri constructed the sequence

$$
1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,1,1,1,1,1,1,2,2,2,2,2,2,2, \ldots
$$

starting with one 1, followed by two 2's, three 3's, four 4's, five 5's, six 1's, seven 2's, and so on. What is the 100th term in this sequence?

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