
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 triangle has a fixed base $AB$ that is $6$ inches long. The median from $A$ to side $BC$ is $4$ inches long and must be at a 60-degree angle with the base. Determine the locus of vertex $C$.
A) A circle with center A and radius 6 inches
B) A circle with center A and radius 7 inches
C) An ellipse with A as focus
D) A straight line perpendicular to AB at A

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