
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 $\overrightarrow{a}=(2\cos x,\sin x)$ and $\overrightarrow{b}=(\cos x,2 \sqrt {3}\cos x)$, and the function $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}-1$.
- (Ⅰ) Find the interval of monotonic decrease for the function $f(x)$;
- (Ⅱ) In an acute triangle $ABC$, with the sides opposite to angles $A$, $B$, and $C$ being $a$, $b$, and $c$ respectively, and $\tan B= \frac { \sqrt {3}ac}{a^{2}+c^{2}-b^{2}}$, find the range of values for $f(A)$ for any angle $A$ that satisfies the condition.

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