
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 the inequality
$$
2 \sin^2 C + \sin A \cdot \sin B > k \sin B \cdot \sin C
$$
holds for any triangle \( \triangle ABC \), then the maximum value of the real number \( k \) is .

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