
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
If the line \( x = \frac{\pi}{4} \) intercepts the curve \( C: (x - \arcsin a)(x - \arccos a) + (y - \arcsin a)(y + \arccos a) = 0 \) at a chord of length \( d \), find the minimum value of \( d \) as \( a \) varies.

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