
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 two four-digit numbers \( M \) and \( N \) which are reverses of each other, and have \( q^{p}-1 \) identical positive divisors, \( M \) and \( N \) can be factorized into prime factors as \( p q^{q} r \) and \( q^{p+q} r \) respectively, where \( p \), \( q \), and \( r \) are prime numbers. Find the value of \( M \).

(Note: Numbers such as 7284 and 4827 are reverses of each other).

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