
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 variation rules of two sound waves over time are respectively $y_1=3\sqrt{2}\mathrm{sin}(100\pi t)$ and $y_2=3\mathrm{sin}(100\pi t-\frac{\pi }{4})$, calculate the amplitude of the combined sound wave, $y=y_1+y_2$.

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