
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 $(2)_x-3)^{4}=$ _$(a)_{0}+$ _$(a)_{1}x+$ _$(a)_{2}x^{2}+$ _$(a)_{3}x^{3}+$ _$(a)_{4}x^{4}$, find  
$(1)$ _$(a)_{1}+$ _$(a)_{2}+$ _$(a)_{3}+$ _$(a)_{4}$.  
$(2)$ _$(a)_{0}+$ _$(a)_{2}+$ _$(a)_{4})^{2}-($ _$(a)_{1}+$ _$(a)_{3})^{2}$.

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