
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
A lumberjack is building a non-degenerate triangle out of logs. Two sides of the triangle have lengths  $\log 101$  and  $\log 2018$ . The last side of his triangle has side length  $\log n$ , where  $n$  is an integer. How many possible values are there for  $n$ ?

*2018 CCA Math Bonanza Individual Round #6*

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