
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
Evaluate:  
1. $\dfrac {\sin 27 ^{\circ} +\cos 45 ^{\circ} \sin 18 ^{\circ} }{\cos 27 ^{\circ} -\sin 45 ^{\circ} \sin 18 ^{\circ} }$  
2. $2\sin 50^{\circ}+\sin 10^{\circ}(1+ \sqrt {3}\tan 10^{\circ}) \sqrt {2\sin ^{2}80 ^{\circ} }$．

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