
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 that the quadratic function \( f(x) = ax^2 + bx + c \) satisfies \( f(5-x) = f(5+x) \) and \( a > 0 \), arrange the three function values \( f(\sqrt{40}) \), \( f(2\pi) \), \( f\left(5 \sin 45^\circ\right) \) in ascending order.

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