
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
In triangle \( \triangle ABC \), \(a, b, c\) are the sides opposite to the angles \(A, B, C\) respectively. Given that \( 7b^2 + 25c^2 - 25a^2 = 0 \), find the value of \( \sin(2A - C) \) when \( A - C \) is at its maximum.

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