
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 lucky number is a number whose digits are only  $4$  or  $7.$  What is the  $17$ th smallest lucky number?

*Author: Ray Li*

<details><summary>Clarifications</summary>[list=1][*]Lucky numbers are positive.
[*]"only 4 or 7" includes combinations of 4 and 7, as well as only 4 and only 7. That is, 4 and 47 are both lucky numbers.[/list]</details>

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