
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 $\overrightarrow {e_{1}}$ and $\overrightarrow {e_{2}}$ are two non-collinear non-zero vectors in a plane, $\overrightarrow {AB}=2 \overrightarrow {e_{1}}+ \overrightarrow {e_{2}}$, $\overrightarrow {BE}=- \overrightarrow {e_{1}}+\lambda \overrightarrow {e_{2}}$, $\overrightarrow {EC}=-2 \overrightarrow {e_{1}}+ \overrightarrow {e_{2}}$, and points A, E, C are collinear.  
(1) Find the value of the real number $\lambda$;  
(2) If $\overrightarrow {e_{1}}=(2,1)$, $\overrightarrow {e_{2}}=(2,-2)$, find the coordinates of $\overrightarrow {BC}$.

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