
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 the arithmetic sequence \(\{a_n\}\) have a common difference \(d\), with \(d \neq 0\). The sequence \(\{b_n\}\) is a geometric sequence with a common ratio \(q\), such that \(a_1 = b_1\), \(a_3 = b_3\), and \(a_7 = b_5\). Find the relationship between \(n\) and \(m\) such that \(a_n = b_m\).

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