
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
Cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ has an edge length of $a$. Point $E$ is the midpoint of $C D$, and point $F$ is the midpoint of $A A_{1}$. Determine the area of the cross-section that passes through points $E$, $F$, and $B_{1}$.

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