
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 that $|a|=10$, $|b|=12$, and the angle between $a$ and $b$ is $120^{\circ}$, find:

1. $a\cdot b$;
2. $\left(3a\right)\cdot\left(\frac{1}{5}b\right)$;
3. $\left(3b-2a\right)\cdot\left(4a+b\right)$.

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