
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 function \( f(x) = a \sin x + b \cos x + c \), its graph passes through the points \( A(0, 5) \) and \( B\left(\frac{\pi}{2}, 5\right) \). For \( 0 \leqslant x \leqslant \frac{\pi}{2} \), the condition \( |f(x)| \leqslant 10 \) holds. Find the range of values for \( c \).

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