
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 the planar vectors $\overrightarrow{a}=(1,x)$ and $\overrightarrow{b}=(2x+3,-x)$ where $x \in \mathbb{R}$.
(1) If $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$, find $|\overrightarrow{a}-\overrightarrow{b}|$.
(2) If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is acute, find the range of values for $x$.
(3) If $|\overrightarrow{a}|=2$, find the coordinates of the unit vector $\overrightarrow{c}$ that is perpendicular to $\overrightarrow{a}$.

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