
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 the function $f(x) = m\sin{x} + \cos{x}$ ($x \in \mathbb{R}$) whose graph passes through the point $(\frac{\pi}{2}, 1)$,
(1) Determine the explicit formula of $y = f(x)$, and find the function's smallest positive period and maximum value;
(2) How to obtain the graph of the function $f(2x)$ from the graph of the function $f\left(x - \frac{\pi}{4}\right)$.

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