
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
The engines of a rocket launched vertically upwards from the Earth's surface, providing an acceleration of $20 \mathrm{~m/s}^2$, suddenly stopped working 40 seconds after the launch. What is the maximum height the rocket will reach? Could this rocket pose a danger to an object located at a height of 45 km? Ignore air resistance, and consider the acceleration due to gravity as $10 \mathrm{~m/s}^2$.

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