
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 $\mathbf{m}$ be the midpoint of $2\mathbf{a}$ and $\mathbf{b}$. Given $\mathbf{m} = \begin{pmatrix} -1 \\ 5 \end{pmatrix}$ and $\mathbf{a} \cdot \mathbf{b} = 10$, find $\|\mathbf{a}\|^2 + \|\mathbf{b}\|^2.$

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