
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
When Ray attempts to climb stairs $m$ steps at a time, starting from the floor (step 0), he jumps to step $m$ then to $2m$ and so forth until the remaining steps to the top are less than $m$. Ray climbs a flight of stairs $n$ steps in two ways. Firstly, when he climbs $6$ steps at a time, there are $4$ steps left at the top. Secondly, when he climbs $7$ steps at a time, there are $3$ steps left at the top. Determine the smallest possible value of $n$ that is greater than $10$.

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