
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 base of the pyramid is a parallelogram \(ABCD\) with an area of \(m^2\). It is known that \(BD \perp AD\). The dihedral angles at the edges \(AD\) and \(BC\) are \(45^{\circ}\), and at the edges \(AB\) and \(CD\) are \(60^{\circ}\). Find the lateral surface area and the volume of the pyramid.

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