
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
Ray climbs up a flight of stairs of $n$ steps in three different ways. When he climbs it $6$ steps at a time, there are $4$ steps left at the top. When he climbs it $7$ steps at a time, there are $3$ steps left at the top. Additionally, when he climbs it $8$ steps at a time, there are $5$ steps left at the top. What is the smallest possible value of $n$ that is greater than $20$?

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