
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
Let $\beta$ be an angle in radians. Determine the value of $k$ if:
\[
(\sin \beta + \sec \beta)^2 + (\cos \beta + \csc \beta)^2 = k + \sin^2 \beta + \cos^2 \beta + \sec^2 \beta + \csc^2 \beta.
\]

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