
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
A circle is given with center $S$ and radius $39 \mathrm{~mm}$. We need to inscribe a triangle $ABC$ in the circle such that the side $AC$ has a length of $72 \mathrm{~mm}$ and point $B$ lies in the half-plane determined by the line $AC$ and point $S$.

From the given information, calculate the height of triangle $ABC$ from vertex $B$ such that the problem has two solutions. Describe all possibilities.

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