
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 the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) with \(a > b > 0\), and its center \(O\), draw two perpendicular chords \(AC\) and \(BD\). Let the eccentric angles of points \(A\) and \(B\) be \(\theta_{1}\) and \(\theta_{2}\) respectively (i.e., the coordinates of point \(A\) are \(\left(a \cos \theta_{1}, b \sin \theta_{1}\right)\)). Find the range of the value of \(\left|\cos \left(\theta_{1}-\theta_{2}\right)\right|\).

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