
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 $y=a (0 < a < 1)$ and the function $f(x)=\sin \omega x$ intersect at 12 points on the right side of the $y$-axis. These points are denoted as $(x\_1)$, $(x\_2)$, $(x\_3)$, ..., $(x\_{12})$ in order. It is known that $x\_1= \dfrac {\pi}{4}$, $x\_2= \dfrac {3\pi}{4}$, and $x\_3= \dfrac {9\pi}{4}$. Calculate the sum $x\_1+x\_2+x\_3+...+x\_{12}$.

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