
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 $\mathbf{a} = \begin{pmatrix} 2 \\ -3 \\ 1 \end{pmatrix},$ $\mathbf{b} = \begin{pmatrix} -1 \\ 0 \\ 4 \end{pmatrix},$ and $\mathbf{c} = \begin{pmatrix} 0 \\ 5 \\ -2 \end{pmatrix}.$ Find the angle between the vectors $\mathbf{a}$ and $(\mathbf{a} \cdot \mathbf{c}) \mathbf{b} - (\mathbf{a} \cdot \mathbf{b}) \mathbf{c}$ in degrees.

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