
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 the binary operations $\diamondsuit$ and $\heartsuit$ defined by $a \, \diamondsuit \, b = a^{\log_{7}(b)}$ and $a  \, \heartsuit \, b = a^{\frac{1}{\log_{7}(b)}}$, and the recursively defined sequence $(a_n)$, where $a_3 = 3\, \heartsuit\, 2$ and $a_n = (n\, \heartsuit\, (n-1)) \,\diamondsuit\, a_{n-1}$ for integers $n \geq 4$, find $\log_{7}(a_{2019})$.

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