
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
On May 1st, Xiaotong and her mother agreed to depart from Oupeng Central Park and travel along the same route to Binjiang Park, which is $4320$ meters away. It is known that Xiaotong's mother walks at a speed that is $1.2$ times that of Xiaotong.<br/>$(1)$ If Xiaotong departs $12$ minutes earlier than her mother from Oupeng Central Park and they both arrive at Binjiang Park at the same time, what is the speed of Xiaotong's mother in meters per minute?<br/>$(2)$ After Xiaotong's careless mother arrives at Binjiang Park, she remembers that there is a team-building activity at her company in $30$ minutes, and the company is $2940$ meters away from Binjiang Park. She immediately sets off from Binjiang Park to the company. She walks at her original speed for a period of time and then runs at a speed of $150$ meters per minute. If she does not want to be late, how many minutes at least does she need to run?

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