
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
A sequence of numbers arranged according to a certain rule is as follows: $3$, $-\frac{5}{3}$, $\frac{9}{5}$, $-\frac{17}{7}$, $\frac{33}{9}$, $-\frac{65}{11}$, $\ldots$ Following this pattern, the $10$th number is ______.

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