
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 two axes, $Ox$ and $Oy$, intersecting at a $60^{\circ}$ angle in a plane, with $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ being unit vectors in the positive directions of the $x$ and $y$ axes respectively. If $\overrightarrow{OP}=x\overrightarrow{e_{1}}+y\overrightarrow{e_{2}}$, then the ordered pair $(x, y)$ is called the coordinate of vector $\overrightarrow{OP}$ in the coordinate system $xOy$. Assuming $\overrightarrow{OP_{1}}=(2,3)$ and $\overrightarrow{OP_{2}}=(3,2)$, find $| \overrightarrow{P_{1}P_{2}}|$ = \_\_\_\_\_\_.

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