
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
At the International Congress of Mathematicians held in Beijing in 2002, the emblem was designed based on the "Chords Diagram" originated by the ancient Chinese mathematician Zhao Shuang. The diagram consists of four congruent right-angled triangles and a small square combined to form a larger square (as shown in the diagram). If the area of the small square is 1 and the area of the large square is 25, and the smaller acute angle in the right-angle triangle is $\theta$, then the value of $\cos 2\theta$ is equal to ______.

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