
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
Given \( a_{1}=5 \) and \( a_{i} \) (\(i=1,2, \cdots\)) are all natural numbers, satisfying the conditions \( a_{1}<a_{2}<\cdots<a_{n}<\cdots \) and \( a_{i+a}=2 a_{i} \) (\(i=1,2, \cdots\)), find \( a_{1993} \).

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