
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
Given a cube  $ABCDA_1B_1C_1D_1$   with edge  $5$ . On the edge  $BB_1$  of the cube , point  $K$  such thath  $BK=4$ .
a) Construct a cube section with the plane  $a$  passing through the points  $K$  and  $C_1$   parallel to the diagonal  $BD_1$ .
b) Find the angle between the plane  $a$  and the plane  $BB_1C_1$ .

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