
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) Calculate: $\sqrt{2}+(\frac{1}{2})^{-2}+(-1)^0-2\sin45^\circ$
2) Find the positive integer solutions for $x$ and $y$ that satisfy the system of equations: 
$$
\begin{cases} 
2x+y=15 \\
y+7x\leq 22 
\end{cases}
$$

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