
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 $$\overrightarrow{a} = (2\lambda\sin x, \sin x + \cos x)$$ and $$\overrightarrow{b} = (\sqrt{3}\cos x, \lambda(\sin x - \cos x))$$ ($\lambda > 0$), the maximum value of the function $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$ is 2.

(Ⅰ) Find the interval of monotonic decrease for the function $f(x)$.

(Ⅱ) In triangle ABC, with the sides opposite to angles A, B, and C being a, b, and c respectively, and $\cos A = \frac{2b-a}{2c}$, if $f(A) - m > 0$ always holds, find the range of the real number $m$.

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