
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 \(\mathbf{a}\) and \(\mathbf{b}\) be vectors, and let \(\mathbf{n}\) be the midpoint of \(\mathbf{a}\) and \(\mathbf{b}\). Given \(\mathbf{n} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}\) and \(\mathbf{a} \cdot \mathbf{b} = 10\), find \(\|\mathbf{a}\|^2 + \|\mathbf{b}\|^2.\)

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