
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
Observe the following data and fill in the appropriate numbers on the blanks according to a certain rule: $1$,$-\frac{3}{4}$,$\frac{5}{9}$,$-\frac{7}{16}$,$\frac{9}{25}$,______,______,$\ldots $The $n$th number is ______.

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