
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 four distinct positive numbers $a$, $b$, $c$, $d$ form an arithmetic sequence, determine the relationship between the midpoint of the first and last terms and the geometric mean of the middle two terms.

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