
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 generated by the vectors \( \mathbf{u} \) and \( \mathbf{v} \), where the area generated by vectors \( \mathbf{a} \) and \( \mathbf{b} \) is 20. If the new vectors are defined as \( \mathbf{u} = \frac{1}{2} \mathbf{a} + \frac{5}{2} \mathbf{b} \) and \( \mathbf{v} = 3 \mathbf{a} - 2 \mathbf{b} \), find the resulting parallelogram's area.

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