
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 probabilities of heads and tails be \( p \) and \( q = 1 - p \), respectively. Form the equation

\[ C_{10}^{5} p^{5} q^{5}=C_{10}^{6} p^{6} q^{4} \]

from which we find: 
\[ 252 q = 210 p \]
\[ \frac{p}{q} = \frac{6}{5} \]
\[ p = \frac{6}{11} \]

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