
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
Tiles are laid on the ground of a rectangle, with the length of the rectangle's ground being $\sqrt{128}m$ and the width being $\sqrt{75}m$.  
$(1)$ Find the perimeter of the rectangle's ground;  
$(2)$ It is planned to cover the entire ground of the rectangle with tiles. Calculate the total area of tiles needed (Hint: approximate results with integers $\sqrt{10}\approx 3.2$, $\sqrt{6}\approx 2.4$).

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