
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 $3 \vec{a} + 4 \vec{b} + 5 \vec{c} = 0$ and $|\vec{a}| = |\vec{b}| = |\vec{c}| = 1$, find the value of $\vec{a} \cdot (\vec{b} + \vec{c})$.

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