
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
Simplify and calculate:

1. $\sin 50^{\circ}(1+ \sqrt {3}\tan 10^{\circ})$;
2. Given $\cos (α- \dfrac {β}{2})=- \dfrac {1}{3}$, $α∈( \dfrac {π}{2},π)$, $\sin ( \dfrac {α}{2}-β)= \dfrac { \sqrt {6}}{3}$, $β∈(0, \dfrac {π}{2})$, find the value of $\cos (α+β)$.

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