
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 $(1-x)^{5}={a}\_{0}+{a}\_{1}x+{a}\_{2}x2+{a}\_{3}{x}^{3}+{a}\_{4}{x}^{4}+{a}\_{5}{x}^{5}$, determine the value of $({a}\_{0}+{a}\_{2}+{a}\_{4})({a}\_{1}+{a}\_{3}+{a}\_{5})$.

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