
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

It is known that the tangents to the graph of the target function \( y=a(x+2)^2 + 2 \) drawn from the point \( M(x_0, y_0) \) intersect at a right angle. Restore the form of the target function, given that the coordinates of the point \( M(x_0, y_0) \) satisfy the relationship:

\[ 
\log_{x-x^2+3}(y-6) = \log_{x-x^2+3} \frac{|2x+6| - |2x+3|}{3x+7.5} \sqrt{x^2 + 5x + 6.25} 
\]

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