
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
(1) Given that $\alpha$ and $\beta$ are acute angles, and $\cos\alpha= \frac{1}{7}$, $\cos(\alpha+\beta)=- \frac{11}{14}$, find $\beta$;  
(2) Given that $\tan\left( \frac{\pi}{4}+\alpha\right)= \frac{1}{2}$, calculate the value of $\frac{\sin2\alpha-\cos^2\alpha}{1+\cos2\alpha}$.

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