
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 exponential sequence $\{a_{n}\}$, where $a_{2}=2$ and $a_{5}=\frac{1}{4}$, find the maximum positive integer $n$ that satisfies the inequality $a_{1}a_{2}+a_{2}a_{3}+\ldots +a_{n}a_{n+1}\leqslant \frac{{21}}{2}$.

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