
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
A rectangular piece of paper 7 inches wide is folded as in a similar diagram so that one corner touches the opposite side. The paper has an additional flap that extends 2 inches perpendicular from the original fold, altering the angle. If the angle $\phi$ at which the extension fold protrudes coincides with angle $\theta$ for the original fold to touch the opposite side, determine the length in inches of the newer, extended crease $M$ in terms of angle $\theta$.
A) $7\sec{\theta} + 2\sin{\theta}$  
B) $7\tan{\theta} + 2\cos{\theta}$  
C) $7\sec^2{\theta} + 2\sin\theta$  
D) $7\tan\theta + 2\sec\theta$

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