
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 $\sin\alpha + \cos\alpha = \frac{7}{13}$, with $\alpha \in (0, \pi)$, find the value of $\tan\alpha$.
2. Find the minimum value for $y=\sin 2x + 2\sqrt{2}\cos\left(\frac{\pi}{4}+x\right)+3$.

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