
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 each $a_{i}$ (for $i=1, 2, \ldots$) is a natural number, satisfying $a_{1}<a_{2}<\cdots<a_{n}<\cdots$ and $a_{i+a}=2 a_{i}$ (for $i=1, 2, \cdots$), find $a_{1993}$.

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