
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
\[
\left(\sin 160^{\circ} + \sin 40^{\circ}\right)\left(\sin 140^{\circ} + \sin 20^{\circ}\right) + \left(\sin 50^{\circ} - \sin 70^{\circ}\right) \times \left(\sin 130^{\circ} - \sin 110^{\circ}\right) = 1
\]

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