
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 vectors $a=(1, x)$ and $b=(2x+3, -x)$, where $x \in \mathbb{R}$:
1. Find the value of $x$ if $a$ is perpendicular to $b$.
2. Find the magnitude of the difference between $a$ and $b$ if $a$ is parallel to $b$.

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