
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 $\overrightarrow{a} = (\sin x, \cos x)$, $\overrightarrow{b} = (\sin x, \sin x)$, and $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$

(1) If $x \in \left[-\frac{\pi}{4}, \frac{\pi}{4}\right]$, find the range of the function $f(x)$.

(2) Let the sides opposite the acute angles $A$, $B$, and $C$ of triangle $\triangle ABC$ be $a$, $b$, and $c$, respectively. If $f(B) = 1$, $b = \sqrt{2}$, and $c = \sqrt{3}$, find the value of $a$.

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