
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 side of the base of a regular triangular prism is less than the lateral edge and is equal to \(a\). A plane is passed through a side of the top base, forming a \(45^{\circ}\) angle with the base plane and dividing the prism into two parts. Determine the volume and the total surface area of the upper part of the prism.

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