
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
In a right-angled triangle, let \( s_{a} \) and \( s_{b} \) be the medians to the legs, and \( s_{c} \) be the median to the hypotenuse. Determine the maximum value of the expression \( \frac{s_{a} + s_{b}}{s_{c}} \).

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