
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 $(1-x)^{n}=1+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+…+a_{n}x^{n}(n∈N^{∗})$ and $a_{1}$:$a_{3}=1$:$7$, determine the value of $a_{5}$.

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