
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
In a manner similar to the Cartesian coordinate system, a coordinate system on a plane formed by two intersecting but not perpendicular axes (with the origin of the two axes overlapping at point $O$ and having the same unit length) is called an oblique coordinate system. In the oblique coordinate system $xOy$, if $\vec{OP} = x \vec{e}_1 + y \vec{e}_2$ (where $\vec{e}_1$ and $\vec{e}_2$ are the unit vectors in the positive directions of the $x$-axis and $y$-axis, respectively, and $x, y \in \mathbb{R}$), then the coordinates of point $P$ are $(x, y)$. If in the oblique coordinate system $xOy$, $\angle xOy = 60^\circ$, and the coordinates of point $M$ are $(1, 2)$, then the distance from point $M$ to the origin $O$ is ______.

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