
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 the triangle \(\triangle ABC\), the side lengths opposite to angles \(A\), \(B\), and \(C\) are \(a\), \(b\), and \(c\) respectively. If \(c - a\) equals the height \(h\) from angle \(A\) to side \(AC\), calculate the value of \(\sin \frac{C - A}{2} + \cos \frac{C + A}{2}\).

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