
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
By analogy with the cosine theorem, in $\triangle DEF$, we have the cosine theorem: $DE^2 = DF^2 + EF^2 - 2DF \cdot EF \cdot \cos \angle DFE$. Extending to space, by analogy with the cosine theorem for triangles, write out the relationship between the areas of the 3 side faces in the oblique prism $ABC-A_1B_1C_1BC$ (where $\theta$ is the dihedral angle formed by the planes of the side faces $ABB_1A_1$ and $BCC_1B_1$).

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