
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 hyperbola $$C: \frac{x^{2}}{a^{2}} - \frac{y^{2}}{4} = 1 (a > 0)$$ whose foci coincide with the two vertices of the ellipse $$\frac{x^{2}}{16} + \frac{y^{2}}{8} = 1$$.

1. Find the coordinates of the foci of hyperbola C and the length of its real axis.
2. If line $l$ intersects hyperbola C at points A and B, and the midpoint of segment AB is (6, 1), find the equation of line $l$.

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