
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 string of $n$ $8$'s, $8888\cdots88,$ into which $+$ signs are inserted to produce an arithmetic expression. For example, $8+88+888+8+8=900$ could be obtained from eight $8$'s in this way. For how many values of $n$ is it possible to insert $+$ signs so that the resulting expression has value $8000$?

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