
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 constructed on the vectors \( \mathbf{a} \) and \( \mathbf{b} \).

\[
\mathbf{a} = 3\mathbf{p} - 2\mathbf{q}
\]

\[
\mathbf{b} = \mathbf{p} + 5\mathbf{q}
\]

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

\[
|\mathbf{q}| = \frac{1}{2}
\]

\[
(\widehat{\mathbf{p}, \mathbf{q}}) = \frac{5\pi}{6}
\]

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