
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 $\angle AOB=60^{\circ}$, 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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