
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
In the Cartesian coordinate system $xOy$, if the curve $y=ax^{2}+ \frac{b}{x}$ (where $a,b$ are constants) passes through point $P(2,-5)$, and the tangent line to the curve at point $P$ is parallel to the line $7x+2y+3=0$, then the value of $a+b$ is.

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