
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 \(\overline{CH}\) be an altitude of \(\triangle ABC\). Let \(R\) and \(S\) be the points where the circles inscribed in the triangles \(ACH\) and \(BCH\) are tangent to \(\overline{CH}\). If \(AB = 2021\), \(AC = 2020\), and \(BC = 2019\), then \(RS\) can be expressed as \(\frac{m}{n}\), where \(m\) and \(n\) are relatively prime integers. Find \(m + n\).

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