
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 a rectangular parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$, the diagonal $C A_{1}$, which is equal to $d$, is inclined at an angle of $60^{\circ}$ to the base plane and forms an angle of $45^{\circ}$ with the plane passing through the diagonal $A C_{1}$ and the midpoint of the side edge $B B_{1}$. Find the area of the base of the parallelepiped.

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