
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 vectors $a$ and $b$ are in the same plane, where $a=(1,2)$ and $|\mathbf{b}|=2\sqrt{5}$.

(Ⅰ) If $a\parallel b$, find the coordinates of vector $b$;

(Ⅱ) If $(2a-3b)\cdot(2a+b)=-20$, find the value of the angle $\theta$ between $a$ and $b$.

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