
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
Define the sequence of positive integers \(\{a_n\}\) as follows. Let \(a_1 = 1\), \(a_2 = 3\), and for each \(n > 2\), let \(a_n\) be the result of expressing \(a_{n-1}\) in base \(n-1\), then reading the resulting numeral in base \(n\), then adding \(2\) (in base \(n\)). For example, \(a_2 = 3_{10} = 11_2\), so \(a_3 = 11_3 + 2_3 = 6_{10}\). Express \(a_{2013}\) in base ten.

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