
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 $\overrightarrow{a} = (\cos{\theta} - 2\sin{\theta}, 2)$ and $\overrightarrow{b} = (\sin{\theta}, 1)$:
(Ⅰ) If $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$, find the value of $\tan{2\theta}$;
(Ⅱ) Let $f(\theta) = (\overrightarrow{a} + \overrightarrow{b}) \cdot \overrightarrow{b}$, with $\theta \in [0, \frac{\pi}{2}]$, determine the range of the function $f(\theta)$.

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