
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
Suppose you want to arrange a string of $n$ $7$'s, such as $777\cdots7$, by inserting $+$ signs to yield an arithmetic expression. For instance, you could form $77+77+7 = 161$ from seven $7$'s. For how many values of $n$ is it feasible to insert $+$ signs so that the resulting numerical expression equals $6300$?

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