
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 $f(x)=\sin x\cos x+\cos ^2x$.
(Ⅰ) Find the smallest positive period of the function $f(x)$, and write down the equation of the axis of symmetry for the graph of $f(x)$.
(Ⅱ) If the graph of the function $y=f(x)$ is translated to the right by $\dfrac{\pi}{8}$ units to obtain the graph of the function $y=g(x)$, find the set of real numbers $x_0$ that satisfy $g(x_0)\geqslant 1$.

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