
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
Let $ABCD$ be a rectangle with $AB = 24$ and $BC = 10$. Let $M$ be a point on side $BC$, and let $R$ and $S$ be the feet of the perpendiculars from $M$ to diagonal $AC$ and side $AD$, respectively. Find the minimum possible value of $RS$.

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