
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 the function $f\left(x\right)=4\cos x\sin \left(x-\frac{π}{3}\right)+a$ with a maximum value of $2$.

(1) Find the value of $a$ and the minimum positive period of the function $f\left(x\right)$;

(2) In $\triangle ABC$, if $A < B$, and $f\left(A\right)=f\left(B\right)=1$, find the value of $\frac{BC}{AB}$.

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