
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 car travels due east at $1$ mile per minute on a long, straight road. Simultaneously, a circular storm with a radius of $60$ miles moves southeast at $\frac{3}{\sqrt{2}}$ miles per minute. At time $t=0$, the center of the storm is $150$ miles due north of the car. At time $t=t_1$ minutes, the car enters the storm circle, and at time $t=t_2$ minutes, the car leaves the storm circle. Find $\frac{1}{2}(t_1+t_2)$.

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