
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 an isosceles triangle $ABC$ where $AB = AC$, the equation of the line on which $AB$ lies is $2x + y - 4 = 0$, and the equation of the median AD on side $BC$ is $x - y + 1 = 0$, with $D$ as point $(4, 5)$.
(Ⅰ) Find the equation of line $BC$.
(Ⅱ) Determine the coordinates of point $B$ and the equation of the line on which side $AC$ lies.

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