
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 $$f(x)=\cos^{2}(\omega x+\varphi)- \frac {1}{2}$$, where $$(\omega>0，0<\varphi< \frac {\pi}{2})$$. If the smallest positive period of $f(x)$ is $\pi$, and $$f\left( \frac {\pi}{8}\right)= \frac {1}{4}$$.

（Ⅰ）Find the values of $\omega$ and $\varphi$;  
（Ⅱ）Find the minimum and maximum values of the function $f(x)$ in the interval $$\left[ \frac {\pi}{24}， \frac {13\pi}{24}\right]$$.

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