
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
Calculate the area of the parallelogram formed by the vectors \( \mathbf{a} \) and \( \mathbf{b} \).

\[ \mathbf{a} = 3\mathbf{p} - \mathbf{q} \]

\[ \mathbf{b} = \mathbf{p} + 2\mathbf{q} \]

\[ |\mathbf{p}| = 3 \]

\[ |\mathbf{q}| = 4 \]

\[ (\widehat{\mathbf{p}, \mathbf{q}}) = \frac{\pi}{3} \]

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