
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
If $e^{α+\frac{π}{6}}-e^{-α-\frac{π}{6}}+cos(\frac{5π}{3}+α)=t$, $e^{β-\frac{π}{4}}-e^{\frac{π}{4}-β}+cos(\frac{5π}{4}+β)=-t$, then $\sin \left(\alpha +\beta \right)=$____.

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