
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 equations of one side $AB$ of the rhombus $ABCD$: $x - 3y + 10 = 0$, and one of its diagonals: $x + 4y - 4 = 0$. The diagonals of the rhombus intersect at point $P(0, 1)$. Find the equations of the other sides of the rhombus, the distance from point $P$ to side $AB$, and the internal angles of the rhombus.

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