
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
(1) Simplify $\dfrac { \sqrt {1+2\sin 610 ^{\circ} \cos 430 ^{\circ} }}{\sin 250 ^{\circ} +\cos 790 ^{\circ} }$;  
(2) Given $\sin \alpha+\cos \alpha= \dfrac {2}{3}$, find the value of $\dfrac {2\sin ^{2}\alpha+2\sin \alpha\cos \alpha}{1+\tan \alpha}$.

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