
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 a sequence of $n$ $8$'s, $8888\cdots88,$ where $+$ signs are inserted between some of the $8$'s to create different sums. For instance, you could form $8+88+888+8+8=1000$ using eleven $8$'s. For how many values of $n$ can you insert $+$ signs such that the summation equals $8880$?

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