
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

In the cube \(ABCD EFGH\), with an edge length of \(6 \mathrm{~cm}\), point \(M\) is the midpoint of \(\overline{EF}\).

a) Determine the area of triangle \(AMH\).

b) Determine the volume of the pyramid \(AMHE\). (The volume of a pyramid can be calculated as one third of the product of the area of the base and the height relative to this base.)

c) Calculate the height relative to the base \(AMH\).

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