
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
(本小题13分) Given vectors $m = (\sin x, 1)$ and $n = (\cos x, \cos^2 x)$,  
(1) If $m \cdot n = 1$, find the value of $\cos(-x)$;  
(2) Let $f(x) = m \cdot n$, in triangle $ABC$, where $A$, $B$, and $C$ are the angles opposite to sides $a$, $b$, and $c$ respectively, and it is given that $(2a - c)\cos B = b\cos C$, find the range of values for the function $f(A)$.

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