
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 an increasing geometric sequence $\{a_{n}\}$ with a common ratio greater than $1$ such that $a_{2}+a_{4}=20$, $a_{3}=8$.  
$(1)$ Find the general formula for $\{a_{n}\}$.  
$(2)$ Find $a_{1}a_{2}-a_{2}a_{3}+\ldots +\left(-1\right)^{n-1}a_{n}a_{n+1}$.

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