
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
Let \(\bold{u} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}\) and \(\bold{z} = \begin{pmatrix} 9 \\ -3 \end{pmatrix}\). After \(\bold{z}\) is modified by adding \(\bold{u}\), find the area of the parallelogram with vertices \(\bold{0}\), \(\bold{u}\), \(\bold{z}\), and \(\bold{u} + \bold{z}\).

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