
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 $\{a_n\}$ is an arithmetic sequence with common difference $d$, and $0 < d < 1$, $a_5 \neq \frac{k\pi}{2}$ (where $k \in \mathbb{Z}$), and $\sin^2 a_3 + 2\sin a_5 \cdot \cos a_5 = \sin^2 a_7$, find the value of the common difference $d$.

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