
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 that the sequence $\{a_n\}$ is an arithmetic sequence, then

$a_1-2a_2+a_3=0$,

$a_1-3a_2+3a_3-a_4=0$,

$a_1-4a_2+6a_3-4a_4+5a_5=0$.

Following the pattern of the above three lines, the conclusion for the fourth line is ______________.

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