
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 directly east at $\frac 23$ mile per minute on a straight road. Simultaneously, a circular storm with a radius of $60$ miles moves southeast at $\frac 34\sqrt{2}$ mile per minute. At time $t=0$, the storm's center is $130$ miles directly north of the car. Determine $\frac 12(t_1+t_2)$ where $t_1$ and $t_2$ are the times when the car enters and exits the storm circle, respectively.

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