
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
In the sequence of real numbers $\{a_n\}$, given that $a_1=0$, $|a_2|=|a_1-1|$, $|a_3|=|a_2-1|$, ..., $|a_n|=|a_{n-1}-1|$, calculate the maximum value of $a_1+a_2+a_3+a_4$.

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