
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
The function $y = \sin x$ is given. If we double the vertical coordinates of all points on its graph while keeping the horizontal coordinates unchanged, we obtain the graph $C\_1$. Then, we shift graph $C\_1$ to the right by $\frac{π}{4}$ units along the $x$-axis to obtain graph $C\_2$. Finally, we shift graph $C\_2$ up by one unit along the $y$-axis to obtain graph $C\_3$. Determine the functional expression for graph $C\_3$.

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