
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 $(2x-1)^{5}=a_{0}+a_{1}x+a_{2}x^{2}+\ldots+a_{5}x^{5}$, find:
  (1) $a_{0}+a_{1}+\ldots+a_{5}$;
  (2) $|a_{0}|+|a_{1}|+\ldots+|a_{5}|$;
  (3) $a_{1}+a_{3}+a_{5}$;
  (4) $(a_{0}+a_{2}+a_{4})^{2}-(a_{1}+a_{3}+a_{5})^{2}$.

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