
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:
\[①a+b > 1\];\[②a+b=2\];\[③a+b > 2\];\[④a^{2}+b^{2} > 2\];\[⑤ab > 1\].
Which of the following conditions can imply that "at least one of $a$ and $b$ is greater than $1$"? (Fill in the blank with the serial number, there is only one correct option)

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