
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 $|\vec{a}|=3,|\vec{b}|=2$, and the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{3}$:
1. Find the value of $|3 \vec{a} - 2 \vec{b}|$.
2. If $\vec{c}=3 \vec{a} + 5 \vec{b}$ and $\vec{d}=m \vec{a} - 3 \vec{b}$, determine the value of $m$ such that $\vec{c} \perp \vec{d}$.

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