
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 $\mathbf{w}$ be a vector such that
\[\left\| \mathbf{w} + \begin{pmatrix} 4 \\ 2 \end{pmatrix} \right\| = 10.\]
Find the smallest possible value of $\|\mathbf{w}\|$.

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