
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 $\triangle ABC$, $\tan A= \frac{1}{3}$, $\tan C= \frac{1}{2}$.
(I) Find the size of angle $B$;
(II) Let $\alpha + \beta = B$ ($\alpha > 0, \beta > 0$), find the range of $\sqrt{2}\sin\alpha - \sin\beta$.

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