
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
Given the line $x+ky=0$ $(k \neq 0)$ intersects the graph of the function $f(x) = \frac{(2^{x}-1)(1-2\sin^2 x)}{2^x+1}$ at two different points $A$ and $B$, and given the point $C(9,3)$, determine the coordinates of the point $D(m,n)$ such that $\vec{DA}+\vec{DB}=\vec{CD}$ and find $m + n$.

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