
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 $f(x)=\cos^2x+ \sqrt{3}\sin x\cos x+a$ whose graph passes through the point $\left(\dfrac{\pi}{6},1\right)$.  
(Ⅰ) Find the value of the real number $a$ and the smallest positive period of the function $f(x)$;  
(Ⅱ) Find the minimum value of the function $f(x)$ on the interval $\left[0, \dfrac{\pi}{2}\right]$.

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