
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
Consider the parabola  $ C: y \equal{} x^2$  in the  $ x \minus{} y$  plane. Let  $ l_1$  be the tangent line of  $ C$  with slope  $ \sqrt {3}$  and  $ l_2$  be the tangent line of  $ C$  with negative slope which makes angle  $ 45^\circ$  with  $ l_1$ . Find the area bounded by  $ C,\ l_1$  and  $ l_2$ .

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