
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
\(a_{1}, a_{2}, a_{3}, \ldots\) is an increasing sequence of natural numbers. It is known that \(a_{a_{k}} = 3k\) for any \(k\). Find:
a) \(a_{100}\);
b) \(a_{1983}\).

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