
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 $\overrightarrow {i}$ and $\overrightarrow {j}$ are unit vectors in the same direction as the x-axis and y-axis, respectively, $\overrightarrow {OA_{1}} = \overrightarrow {j}$, $\overrightarrow {OA_{2}} = 5 \overrightarrow {j}$, $\overrightarrow {A_{n-1}A_{n}} = 2 \overrightarrow {A_{n}A_{n+1}}$ (where $n \geq 2$, $n \in \mathbb{N}^{+}$), $\overrightarrow {OB} = 3 \overrightarrow {i} + 3 \overrightarrow {j}$, and $\overrightarrow {B_{n}B_{n+1}} = 2 \overrightarrow {i} + 2 \overrightarrow {j}$ (where $n \in \mathbb{N}^{+}$).  
(I) Find the magnitude of $\overrightarrow {A_{7}A_{8}}$;  
(II) Find the coordinates of $\overrightarrow {OA_{n}}$ and $\overrightarrow {OB_{n}}$.

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