
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
If the line passing through the point $P(2,1)$ intersects the graph of the function $f(x)= \frac{2x+3}{2x-4}$ at points $A$ and $B$, and $O$ is the origin, calculate the value of $( \overrightarrow{OA}+ \overrightarrow{OB})\cdot \overrightarrow{OP}$.

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