
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 \(X=\overline{a_{1} a_{2} \ldots a_{29}}\) (where \(0 \leq a_{k} \leq 9\) and \(a_{1} \neq 0\)), it is known that for every \(k\), the digit \(a_{k}\) occurs in the number exactly \(a_{30-k}\) times (for example, if \(a_{10}=7\), then the digit \(a_{20}\) occurs seven times). Find the sum of the digits of the number \(X\).

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