
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
Observe the following equations:
$$1^3 = 1,$$
$$2^3 = 3 + 5,$$
$$3^3 = 7 + 9 + 11,$$
$$4^3 = 13 + 15 + 17 + 19,$$
$$\dots$$
If the expansion of some number $n^3$ following the above pattern includes the number "2013" on the right side of the equation, then $n =$ _______.

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