
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 parallelepiped \(ABCD A_1 B_1 C_1 D_1\), construct a line \(l\) that passes through the center of symmetry \(H\) of the base \(ABCD\) and intersects the lines \(BC_1\) and \(FB_1\) (where point \(F\) is the midpoint of edge \(AA_1\)).

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