
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 $n$ $5$'s, $5555\cdots5,$ into which $+$ signs are inserted to produce an arithmetic expression. For example, $5+55+555+5+5=625$ could be obtained from six $5$'s in this way. For how many values of \(n\) is it possible to insert $+$ signs so that the resulting expression has value $5750$?

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