
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. At the same time, a circular storm, whose radius is 60 miles, moves southeast at $\sqrt{2}$ miles per minute. At time $t=0$, the center of the storm is 150 miles due north of the car. Determine $\frac{1}{2}(t_1+t_2)$, where $t_1$ and $t_2$ are the times when the car enters and leaves the storm circle, respectively.

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