
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 \( \triangle ABC \), the lengths of the sides opposite angles \( A, B, \) and \( C \) are \( a, b, \) and \( c \) respectively. If \( c - a \) is equal to the height \( h \) from \( AC \), 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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