
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
The distance from point $P(a, 4)$ to the line $x - 2y + 2 = 0$ is $2\sqrt{5}$, and it is situated within the region represented by the inequality $3x + y > 3$. Find the coordinates of point $P$.

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