
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  $n$  7's,  $7777\cdots77$ , into which  $+$  signs are inserted to produce an arithmetic expression. For example,  $7+77+777+7+7=875$  could be obtained from eight 7's in this way. For how many values of  $n$  is it possible to insert  $+$  signs so that the resulting expression has value 7000?

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