
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
(1) Find the equation of line $l$ that passes through point $P(-3, -4)$ and has equal intercepts on the $x$-axis and $y$-axis.
(2) Given that $|\vec{a}| = 4$, $|\vec{b}| = 3$, and $(2\vec{a} - 3\vec{b}) \cdot (2\vec{a} + \vec{b}) = 61$, find the dot product $\vec{a} \cdot \vec{b}$ and the magnitude $|\vec{a} + 3\vec{b}|$.

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