
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
Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ be the three interior angles of $\triangle \mathrm{ABC}$. Find the maximum value of the real number $\lambda$ such that $\frac{1}{\sin A}+\frac{1}{\sin B} \geq \frac{\lambda}{3+2 \cos C}$ always holds.

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