
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 $\overrightarrow {a}$, $\overrightarrow {b}$, $\overrightarrow {c}$ are three vectors in the same plane, where $\overrightarrow {a} = \left(1, \sqrt {3}\right)$.

(I) If $|\overrightarrow {c}| = 4$ and $\overrightarrow {c}$ is parallel to $\overrightarrow {a}$, find the coordinates of $\overrightarrow {c}$.

(II) If $|\overrightarrow {b}| = 1$ and $(\overrightarrow {a} + \overrightarrow {b}) \perp \left(\overrightarrow {a} - \dfrac{5}{2}\overrightarrow {b}\right)$, find the angle $\theta$ between $\overrightarrow {a}$ and $\overrightarrow {b}$.

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