
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 a triangle $\triangle ABC$ with its three interior angles $A$, $B$, and $C$ satisfying: $$A+C=2B, \frac {1}{\cos A}+ \frac {1}{\cos C}=- \frac { \sqrt {2}}{\cos B}$$, find the value of $$\cos \frac {A-C}{2}$$.

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