
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
A light source positioned at point $M$ on a vertical plane illuminates three points $O$, $A$, and $B$ on a horizontal plane. The illumination intensities at these points are proportional to the numbers $\frac{1}{9}$, $\frac{1}{4}$, and $1$, respectively. Find the position of point $M$ by determining the coordinates $OH = x$ and $MH = y$. Given: $OA = a = 200 \mathrm{~m}$ and $OB = b = 100 \mathrm{~m}$.

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