
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 that $α∈\left( \frac{π}{2},π\right) $, and $\sin \left(π-α\right)+\cos \left(2π+α\right)= \frac{ \sqrt{2}}{3} $. Find the values of:

$(1)\sin {α} -\cos {α} .$

$(2)\tan {α} $.

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