
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]


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The altitude drawn from vertex \( C \) of the right triangle \( ABC \) intersects the hypotenuse \( AB \) at point \( D \), and the centroid of triangle \( ACD \) is \( S \). What relationship holds between the segments of the hypotenuse if \( SB = CB \)? Construct the triangle if the common length of these two segments is given.

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