
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 small [ square](https://artofproblemsolving.com/wiki/index.php/Square_(geometry)) is constructed inside a square of [area](https://artofproblemsolving.com/wiki/index.php/Area) 1 by dividing each side of the unit square into $n$ equal parts, and then connecting the [ vertices](https://artofproblemsolving.com/wiki/index.php/Vertex) to the division points closest to the opposite vertices. Find the value of $n$ if the the [area](https://artofproblemsolving.com/wiki/index.php/Area) of the small square is exactly $\frac1{1985}$. 
[AIME 1985 Problem 4.png](https://artofproblemsolving.com/wiki/index.php/File:AIME_1985_Problem_4.png)

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