
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 angles $A$, $B$, $C$ satisfy $A+B+C=π$, construct a triangle with these angles as its internal angles, and let $a$, $b$, $c$ be the sides opposite to angles $A$, $B$, $C$ respectively. According to the sine law and cosine law, we have the equation: $\sin ^{2}A=\sin ^{2}B+\sin ^{2}C-2\sin B\sin C\cos A$. Now, given that angles $A$, $B$, $C$ satisfy $A+B+C=π$, then $(\frac {π}{2}- \frac {A}{2})+(\frac {π}{2}- \frac {B}{2})+(\frac {π}{2}- \frac {C}{2})=π$. By analogy with the previous method, the equation we can obtain is _______.

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