
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 the three internal angles $A$, $B$, and $C$ of triangle $\triangle ABC$ correspond to the sides $a$, $b$, and $c$ respectively, and that the internal angles form an arithmetic progression. If $a=\sqrt{2}$ and $b=\sqrt{3}$, find the value of $\sin C$.

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