
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 that $e\_1$ and $e\_2$ are two non-zero, non-collinear vectors on a plane, $\overrightarrow{AB} = 2e\_1 + e\_2$, $\overrightarrow{BE} = -e\_1 + λe\_2$, $\overrightarrow{EC} = -2e\_1 + e\_2$, and points $A$, $E$, and $C$ are collinear.

(1) Find the value of the real number $λ$;

(2) If $e\_1 = (2, 1)$ and $e\_2 = (2, -2)$, find the coordinates of $\overrightarrow{BC}$;

(3) Given that $D(3, 5)$, under the conditions of (2), if points $A$, $B$, $C$, and $D$ form a parallelogram in counterclockwise order, find the coordinates of point $A$.

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