
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 tangents to the graph of the target function \( y = a(x+1)^{2} + 1 \), drawn from point \( M(x_{0}, y_{0}) \), intersect at a right angle. Restore the form of the target function, knowing that the coordinates of the point \( M(x_{0}, y_{0}) \) satisfy the equation: 

\[ \log_{3x-x^{2}+1}(y-4) = \log_{3x-x^{2}+1} \left( \frac{|2x+4| - |2x+1|}{3x+4.5} \sqrt{x^{2}+3x+2.25} \right). \]

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