
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
Consider a rectangular parallelepiped  $ABCDEFGH$ .
(a) If this parallelepiped is a cube, what is the measure of the angle  $\angle FCH$  ?
(b) Can the lengths of the edges of this parallelepiped be chosen so that the angle  $\angle FCH =45^o$ ?
(c) What are all the values that the measure of the angle  $\angle FCH$  can take ? 
![Image](https://1.bp.blogspot.com/-5IVxknY90No/XzAOpAgAfnI/AAAAAAAAMTQ/Zbmx0oFEwz4lWvJHmQalectcN6o4SM3yACLcBGAsYHQ/s0/OBM%2B2012%2Bp1.jpg)

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