
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 vectors $\overrightarrow{a}$ = $(2\sin x, m)$ and $\overrightarrow{b}$ = $(\sin x + \cos x, 1)$. Let function $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$ for $x \in \mathbb{R}$, and the maximum value of $f(x)$ is $\sqrt{2}$.
(1) Find the value of $m$.
(2) If the graph of $f(x)$ is translated left by $n$ (where $n > 0$) units and then reflected about the y-axis, find the minimum value of $n$.

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