
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
If $\frac{\sqrt{3}}{2 \sqrt{7}-\sqrt{3}}=\frac{2 \sqrt{21}+h}{25}$, find $h$. 

A can do a job in $k$ days, B can do the same job in $(k+6)$ days. If they work together, they can finish the job in $m$ days. Find $m$.

$m$ coins are tossed. If the probability of obtaining at least one head is $p$, find $p$. $\mathrm{P}($ at least one head $)=1-\mathrm{P}($ all tail $)$

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