
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
In the Cartesian coordinate system xOy, it is known that circle C passes through points A(0, 2), O(0, 0), and D(t, 0) (t > 0). M is a moving point on segment AD, and $l_1$, $l_2$ are two perpendicular lines passing through point B(1, 0), where $l_1$ intersects the y-axis at point E, and $l_2$ intersects circle C at points P and Q.
(1) If t = PQ = 6, find the equation of line $l_2$;
(2) If t is the smallest positive integer such that AM ≤ 2BM always holds, find the minimum value of the area of $\triangle EPQ$.

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