
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
Consider the infinite sequence \$1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, \ldots\$, where the first term is 1, the next two terms are both 2, the following three terms are all 3, then the next four terms are all 4, and so on. Let this sequence be denoted by \{a_n\}. If \$a_{n-1} = 7\$ and \$a_n = 8\$, find the value of \$n\$.

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