
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
Four positive integers  $a, b, c, d$  satisfy the condition:  $a < b < c < d$ . For what smallest possible value of  $d$  could the following condition be true: the arithmetic mean of numbers  $a, b, c$  is twice smaller than the arithmetic mean of numbers  $a, b, c, d$ ?

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