
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
In triangle \(ABC\), given \(\sin A \cdot \cos^2 \frac{C}{2} + \sin C \cdot \cos^2 \frac{A}{2} = \frac{3}{2} \sin B\). Find the value of \(\cos \frac{A-C}{2} - 2 \sin \frac{B}{2}\).

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