
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
Let all the firms in a country have a certain rank, which is a natural number. When two firms of ranks $m$ and $n$ merge, a new firm of rank $(m+n)$ is formed. The profit of the new firm will be $m \cdot n$ more than the sum of the profits of the firms that formed it. The profit of a firm of the first rank is 1 unit. Does there exist a rank at which the profit of the firm will be 2016 units?

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