
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 $(x-a)(x+2)^5=a_0+a_1(x+1)+a_2(x+1)^2+...+a_6(x+1)^6$, if $a_0+a_1+a_2+...+a_6=-96$, find the value of $a_4$.

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