
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
Let  $P_0 = (3,1)$  and define  $P_{n+1} = (x_n, y_n)$  for  $n \ge 0$  by   $$ x_{n+1} = - \frac{3x_n - y_n}{2}, y_{n+1} = - \frac{x_n + y_n}{2} $$  Find the area of the quadrilateral formed by the points  $P_{96}, P_{97}, P_{98}, P_{99}$ .

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