
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
Given $a_1 < a_2$, $b_1 < b_2$, the relationship between $a_1b_1 + a_2b_2$ and $a_1b_2 + a_2b_1$ is \_\_\_\_\_\_\_\_.

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