
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 $\mathbf{u}$ and $\mathbf{v}$ be vectors in $\mathbb{R}^3$, and let $\mathbf{n}$ be the midpoint of $\mathbf{u}$ and $\mathbf{v}$. Given $\mathbf{n} = \begin{pmatrix} 4 \\ 2 \\ 3 \end{pmatrix}$ and $\mathbf{u} \cdot \mathbf{v} = 10$, find $\|\mathbf{u}\|^2 + \|\mathbf{v}\|^2.$

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