
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 $f(x) = m(1 + \sin 2x) + \cos 2x$, where $x \in \mathbb{R}$, and the graph of the function $y = f(x)$ passes through the point $(\frac{\pi}{4}, 2)$.

1. Find the value of the real number $m$.
2. Find the minimum value of the function $f(x)$ and the set of $x$ values at which this minimum occurs.

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