
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

Rectangular room \(ABCD\) has mirrors on walls \(AB\) and \(DC\). A laser is placed at \(B\). It is aimed at \(E\) and the beam reflects off of the mirrors at \(E, F,\) and \(G\), arriving at \(H\). The laws of physics tell us that \(\angle BEC = \angle FEG\) and \(\angle BFE = \angle AFG\) and \(\angle FGE = \angle HGD\). If \(AB = 18 \mathrm{~m}\), \(BC = 10 \mathrm{~m}\), and \(HD = 6 \mathrm{~m}\), what is the total length of the path \(BEFGH\) travelled by the laser beam?

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