
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 \(\mathbf{a} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} -4 \\ 3 \end{pmatrix}\). Find the area of the triangle with vertices \(\mathbf{0}, \mathbf{a}, \) and \(\mathbf{b}\), ensuring that the triangle is right-angled.

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