
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 vectors $$\overrightarrow {a}$$ and $$\overrightarrow {b}$$ in the same plane, where $$\overrightarrow {a} = (1, -2)$$ and the magnitude of $$\overrightarrow {b}$$ is $2\sqrt{5}$.

(Ⅰ) If $$\overrightarrow {a}$$ is parallel to $$\overrightarrow {b}$$, find the coordinates of vector $$\overrightarrow {b}$$.

(Ⅱ) If the dot product of $(2\overrightarrow {a} - 3\overrightarrow {b})$ and $(2\overrightarrow {a} + \overrightarrow {b})$ is $-20$, find the value of the angle $\theta$ between $$\overrightarrow {a}$$ and $$\overrightarrow {b}$$.

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