
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
Let $a$ and $b$ be two real numbers, given the following conditions: ① $a + b > 1$; ② $a + b = 2$; ③ $a + b > 2$; ④ $a^2 + b^2 > 2$; ⑤ $ab > 1$. Among these conditions, the ones that can lead to the conclusion "at least one of $a$ and $b$ is greater than 1" are: _____

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