
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 $x \in \mathbb{R}$, vectors $\vec{a} = (x, 1)$, and $\vec{b} = (1, -2)$, with $\vec{a} \perp \vec{b}$, find $|\vec{a}| = ($ ** ** $)$.

A) $\sqrt{5}$
B) $2\sqrt{5}$
C) $10$
D) $\sqrt{10}$

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