
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 a 29-digit number \( x = \overline{a_{1} a_{2} \cdots a_{28} a_{29}} \) (where \( 0 \leq a_{k} \leq 9 \) and \( a_{1} \neq 0 \) for \( k=1,2, \cdots, 29 \)). It is known that for each \( k \), the digit \( a_{k} \) appears \( a_{30-k} \) times in the representation of the number. For example, if \( a_{10} = 7 \), then the digit \( a_{20} \) appears 7 times. Find the sum of the digits of \( x \).
(The 34th Moscow Mathematical Olympiad, 1971)

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