
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 rest energy of a particle be  $E$ . Let the work done to increase the speed of this particle from rest to  $v$  be  $W$ . If  $ W = \frac {13}{40} E $ , then  $ v = kc $ , where  $ k $  is a constant. Find  $10000k$  and round to the nearest whole number.

*(Proposed by Ahaan Rungta)*

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