
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 triangular region is enclosed by the lines with equations $y = 2x + 4$, $y = -3x + 9$, and $y = 2$. Additionally, a point $P$ lies on line $y = 2$ such that it is equidistant from the two vertical lines passing through the vertices of the triangle on this line. Find the area of the triangular region and the coordinates of point $P$. Express the area as a decimal to the nearest hundredth.

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