
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  $\mathcal{R}$  denote the circular region in the  $xy-$ plane bounded by the circle  $x^2+y^2=36$ . The lines  $x=4$  and  $y=3$  divide  $\mathcal{R}$  into four regions  $\mathcal{R}_i ~ , ~i=1,2,3,4$ . If  $\mid \mathcal{R}_i \mid$  denotes the area of the region  $\mathcal{R}_i$  and if  $\mid \mathcal{R}_1 \mid >$   $\mid \mathcal{R}_2 \mid >$   $\mid \mathcal{R}_3 \mid > $   $\mid \mathcal{R}_4 \mid $ , determine  $\mid \mathcal{R}_1 \mid $   $-$   $\mid \mathcal{R}_2 \mid $   $-$   $\mid \mathcal{R}_3 \mid $   $+$   $\mid \mathcal{R}_4 \mid $ .

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