
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
Let Ox and Oy be two axes in a plane intersecting at a 60° angle, and let $$\overrightarrow {e_{1}}$$ and $$\overrightarrow {e_{2}}$$ be unit vectors in the same direction as the positive directions of the x-axis and y-axis, respectively. If $$\overrightarrow {OP}=x \overrightarrow {e_{1}}+y \overrightarrow {e_{2}}$$, then the ordered pair (x, y) is called the coordinates of vector $$\overrightarrow {OP}$$ in the xOy coordinate system. Suppose $$\overrightarrow {OP_{1}}=(2, 3)$$ and $$\overrightarrow {OP_{2}}=(3, 2)$$, then $$|\overrightarrow {P_{1}P_{2}}|$$ equals \_\_\_\_\_\_.

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