
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
(1) Given $\overrightarrow {OA} = \overrightarrow {a}$, $\overrightarrow {OB} = \overrightarrow {b}$, $|\overrightarrow {OB}| = |\overrightarrow {b}| = 2$, $|\overrightarrow {OA}| = |\overrightarrow {a}| = 2$, and $\angle AOB = 60°$, find $|\overrightarrow {a} - \overrightarrow {b}|$.  
(2) Given vectors $\overrightarrow {e_{1}}$ and $\overrightarrow {e_{2}}$ are non-collinear, and real numbers $x$, $y$ satisfy $(3x-4y) \overrightarrow {e_{1}} + (2x-3y) \overrightarrow {e_{2}} = 6 \overrightarrow {e_{1}} + 3 \overrightarrow {e_{2}}$, find $x-y$.

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