
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
Solve the systems of equations:

1) \(\left\{\begin{array}{l}x+y=10^{20} \\ x-y=10^{19}\end{array}\right.\)

2) \(\left\{\begin{array}{l}2a^{3}+3b^{5}=19 \\ 3a^{3}-4b^{5}=20\end{array}\right.\)

3) \(\left\{\begin{array}{l}x+y=(a+1)^{2} \\ x-y=(a-1)^{2} \end{array}\right.\)

4) \(\left\{\begin{array}{l}a^{2}-2ab+b^{2}=0 \\ 2a-b=3\end{array}\right.\)

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