
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

$$
C_{10}^{7} p^{7} q^{3}=C_{10}^{6} p^{6} q^{4}
$$

from which it follows: $120 p=210 q ; \frac{p}{q}=\frac{7}{4} ; p=\frac{7}{11}$.

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