
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
Given the vertices $A(2, 1)$, $B(6, 3)$, and $C(4, 5)$ of a triangle, find:
1. The length of side $AB$.
2. The interior angle at vertex $A$ in radians to an accuracy of 0.01.
3. The equation of the altitude passing through vertex $C$.
4. The equation of the median passing through vertex $C$.
5. The point of intersection of the altitudes of the triangle.
6. The length of the altitude dropped from vertex $C$.
7. The system of linear inequalities that defines the interior region of the triangle.
Draw a diagram.

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